33 citations · 73 across the 23 of their papers we have counts for
4 papers · 1 filter
A martingale view of Blackwell's renewal theorem and its extensions to a general counting process
Daryl J. Daley, Masakiyo Miyazawa
Martingales constitute a basic tool in stochastic analysis; this paper considers their application to counting processes. We use this tool to revisit a renewal theorem and its exte…
Customer sojourn time in GI/G/1 feedback queue in the presence of heavy tails
Sergey Foss, Masakiyo Miyazawa
We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for…
Queue-length balance equations in multiclass multiserver queues and their generalizations
Marko Boon, Onno Boxma, Offer Kella +1
A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epo…
Martingale approach for tail asymptotic problems in the generalized Jackson network
Masakiyo Miyazawa
We study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network (GJN for short), assuming its stability. For the two station case,…